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arxiv: 2509.03460 · v6 · submitted 2025-09-03 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

"Aftereffects'' Phenomenon in ¹¹¹In(rightarrow¹¹¹Cd)-Implanted α-Al₂O₃ Single Crystals: Novel Approach Integrating Experimental Double-Model Analysis with Density-Functional Theory

Germ\'an N. Darriba , Reiner Vianden , Alejandro P. Ayala , Mario Renter\'ia This is my paper

Pith reviewed 2026-05-18 19:15 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci
keywords aftereffectsdynamic hyperfine interactionTDPACalpha-Al2O3density-functional theoryelectric field gradient111Cd probecharge state
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The pith

The aftereffects in 111In-implanted alpha-alumina arise from 111Cd probes at substitutional Al sites whose Cd impurity level occupations fluctuate with temperature.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an experimental double-model analysis of dynamic hyperfine interactions and combines it with density-functional theory to trace the origins of the reversible aftereffects phenomenon seen in TDPAC measurements. It identifies the probe sites and charge states that produce the stable final electric field gradients after the dynamic process ends. A sympathetic reader would care because the work resolves prior controversies over unexpected signals in these implanted crystals by linking the fluctuations directly to electron-capture decay and hole trapping. The analysis further equates the two common dynamic-interaction models so that initial electronic configurations can be extracted at each temperature.

Core claim

The stable final EFG for the expected interaction HFI_u originates from 111Cd probes located at defect-free substitutional Al sites without trapped electron holes across all measured temperatures. Those of the unexpected HFI_d originate from probes at Al sites but with different degrees of occupation of the Cd impurity level. One trapped hole for HFI_u and at least five for HFI_d are responsible for the dynamic regime when the aftereffects are more pronounced. The proposed scenario accounts for the observation of well-defined EFGs when the dynamic regime does not end.

What carries the argument

Double-model analysis of dynamic hyperfine interactions integrated with DFT defect-formation energies versus charge state of the Cd impurity level.

If this is right

  • The equivalence of the two dynamic HFI analysis methods allows extraction of the initial electronic configurations at each temperature.
  • One trapped hole explains the dynamic regime for the expected interaction HFI_u while at least five holes explain it for the unexpected interaction HFI_d.
  • Well-defined EFGs remain observable when the dynamic regime does not end because the final charge state is stable.
  • The temperature reversal of the aftereffects follows directly from changes in occupation of the Cd impurity level.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same combined analysis could be applied to other wide-bandgap oxide hosts to predict how implanted probes respond to electron-capture decay.
  • If the charge-state assignment holds, external electric fields or co-doping might be used to shift the temperature at which the dynamic regime appears.

Load-bearing premise

The two dynamic HFI analysis methods are equivalent and their extracted initial configurations accurately reflect the physical electronic states at each temperature while DFT formation energies correctly map charge-state occupations to the observed EFGs.

What would settle it

A temperature-dependent measurement that directly counts the number of trapped holes at the probe sites, for example by electron paramagnetic resonance, would confirm or refute the assignment of one hole for HFI_u and at least five for HFI_d in the dynamic regime.

Figures

Figures reproduced from arXiv: 2509.03460 by Alejandro P. Ayala, Germ\'an N. Darriba, Mario Renter\'ia, Reiner Vianden.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p031_11.png] view at source ↗
read the original abstract

We develop an experimental double-model analysis, combined with density-functional theory (DFT), to explore the origins of dynamic hyperfine interactions (HFIs) linked to the electron-capture decay ''aftereffects ''(ECAE) phenomenon. This electronic effect, reversible with temperature, has been observed in time-differential perturbed $\gamma$-$\gamma$ angular correlations (TDPAC) experiments on oxides doped with ($^{111}$In (EC)$\rightarrow$)$^{111}$Cd probe atoms. Besides identifying the electronic configuration that yields the stable final electric-field gradient (EFG) after the dynamic process ends, we determine the initial configurations around the probe nucleus and their corresponding EFGs whose fluctuations produce these dynamic HFIs. We demonstrate the equivalence between parameters of the two most widely used methods for analyzing this type of dynamic HFI, enabling us to obtain these initial electronic configurations at each temperature. In this framework, to unravel controversial TDPAC results reported for $^{111}$In-implanted $\alpha$-Al$_2$O$_3$ single crystals, we perform a DFT study of Cd-doped $\alpha$-Al$_2$O$_3$, examining their defect-formation energies, as functions of the Cd impurity level's charge state. We show that the stable final EFG for the expected interaction HFI$_u$ originates from $^{111}$Cd probes located at defect-free substitutional Al sites (without trapped electron holes) across all measured temperatures. Those of the unexpected HFI$_d$ originate from probes at Al sites, but with different degrees of occupation of the Cd impurity level. We show that one trapped hole for HFI$_u$ and at least five for HFI$_d$ are responsible for the dynamic regime when the ''aftereffects'' are more pronounced. The proposed scenario accounts for the observation of well-defined EFGs when the dynamic regime does not end.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper develops a combined experimental double-model analysis of dynamic hyperfine interactions (HFIs) in TDPAC spectra and DFT calculations of defect formation energies in Cd-doped α-Al₂O₃ to interpret the temperature-reversible 'aftereffects' following ¹¹¹In electron-capture decay. It claims equivalence of the two standard dynamic HFI fitting methods, extracts initial electronic configurations at each temperature, and assigns the stable final EFG of the expected interaction HFI_u to defect-free substitutional ¹¹¹Cd sites with no trapped holes, while attributing the unexpected HFI_d to Al sites with varying occupations of the Cd impurity level (one hole for HFI_u and ≥5 holes for HFI_d in the dynamic regime).

Significance. If the central assignments are validated, the work offers a useful framework for linking TDPAC-observed dynamic HFIs to specific charge-state occupations in oxide hosts via integrated modeling and DFT formation energies. The demonstration of parameter equivalence between the two dynamic analysis methods, if rigorously shown, would be a practical contribution for the TDPAC community studying aftereffects.

major comments (2)
  1. [DFT calculations] DFT section: defect-formation energies are computed as a function of Cd impurity level charge state, but the manuscript does not report explicit EFG tensor or quadrupole-frequency calculations for the proposed configurations (zero holes, one hole, or ≥5 holes). Formation energies establish relative stability but do not directly map to the measured EFG magnitudes or signs used to assign HFI_u and HFI_d; quantitative comparison to the experimental quadrupole frequencies is therefore missing.
  2. [Dynamic HFI analysis] Dynamic HFI analysis section: the equivalence of the two dynamic models is invoked to extract unique initial configurations and hole occupations at each temperature. However, the fitting procedure is not shown to be unique once fluctuation rates, number of intermediate states, and damping parameters are allowed to vary simultaneously; non-uniqueness would undermine the one-to-one mapping from fitted parameters to the physical electronic states claimed for HFI_u and HFI_d.
minor comments (2)
  1. The abstract and main text use 'HFI_u' and 'HFI_d' without an early explicit definition of what the subscripts denote; adding a brief parenthetical on first use would improve readability.
  2. Error bars or uncertainty estimates on the extracted EFG values and occupation numbers from the double-model fits are not mentioned; including them would strengthen the comparison to DFT results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the presentation of our combined experimental and DFT analysis of the aftereffects in 111In-implanted α-Al2O3. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [DFT calculations] DFT section: defect-formation energies are computed as a function of Cd impurity level charge state, but the manuscript does not report explicit EFG tensor or quadrupole-frequency calculations for the proposed configurations (zero holes, one hole, or ≥5 holes). Formation energies establish relative stability but do not directly map to the measured EFG magnitudes or signs used to assign HFI_u and HFI_d; quantitative comparison to the experimental quadrupole frequencies is therefore missing.

    Authors: We agree that the manuscript primarily uses DFT defect-formation energies to establish which charge states (zero holes for the stable HFI_u site and ≥5 holes for the dynamic HFI_d regime) are energetically accessible at the relevant temperatures. The experimental EFG magnitudes and signs for HFI_u and HFI_d are obtained directly from the TDPAC spectral fits. While relative stability provides a physically motivated assignment of which configurations correspond to the observed interactions, we acknowledge that an explicit computation of the EFG tensors for these charge states would allow a more quantitative comparison. In the revised manuscript we will add the calculated quadrupole frequencies (and their signs) for the zero-hole, one-hole, and multi-hole configurations using the same supercell and functional setup, and we will tabulate the comparison with the experimental values extracted for HFI_u and HFI_d. revision: yes

  2. Referee: [Dynamic HFI analysis] Dynamic HFI analysis section: the equivalence of the two dynamic models is invoked to extract unique initial configurations and hole occupations at each temperature. However, the fitting procedure is not shown to be unique once fluctuation rates, number of intermediate states, and damping parameters are allowed to vary simultaneously; non-uniqueness would undermine the one-to-one mapping from fitted parameters to the physical electronic states claimed for HFI_u and HFI_d.

    Authors: We appreciate the referee’s caution regarding possible parameter correlations. In the present work the equivalence between the two dynamic models is demonstrated by applying both formalisms to the same set of temperature-dependent spectra and obtaining statistically consistent values for the initial-state populations and the final EFGs. To test uniqueness we have performed repeated fits starting from widely different initial guesses for the fluctuation rates and damping parameters while keeping the number of intermediate states fixed by the physical model (hole trapping/detrapping). The extracted initial electronic configurations converge to the same temperature-dependent hole occupations within the experimental uncertainties. In the revision we will add a dedicated subsection (or supplementary note) that reports these robustness checks, including the range of starting parameters explored and the resulting spread in the fitted initial configurations, thereby documenting that the mapping to the physical charge states remains unique under the constraints imposed by the data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation combines independent experimental fitting with DFT stability analysis

full rationale

The paper demonstrates equivalence of two dynamic HFI models within its own analysis to extract initial configurations from TDPAC spectra, then applies DFT formation energies versus charge state to interpret which electronic occupations correspond to the observed stable EFGs for HFI_u and HFI_d. No step reduces by construction to a fitted parameter renamed as a prediction, nor relies on a self-citation chain for the central assignment; the DFT component provides external grounding via computed formation energies, and the experimental models are shown equivalent rather than assumed. The overall chain remains self-contained against the input spectra and calculations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on fitted EFG parameters extracted from experimental spectra and on standard DFT assumptions for defect energies; no new particles or forces are postulated.

free parameters (2)
  • EFG magnitudes for initial configurations
    Extracted by fitting the double-model to temperature-dependent TDPAC spectra to match observed dynamic interactions.
  • Trapped-hole occupation numbers
    Assigned as one for HFI_u and at least five for HFI_d to reconcile DFT formation energies with the dynamic regime data.
axioms (2)
  • domain assumption Fluctuations between discrete electronic configurations produce the observed dynamic hyperfine interactions.
    Invoked when applying the double-model analysis to TDPAC time spectra.
  • domain assumption DFT defect-formation energies versus charge state accurately rank the stability of different Cd impurity occupations.
    Used to assign which charge states correspond to the stable and dynamic EFGs.

pith-pipeline@v0.9.0 · 5933 in / 1372 out tokens · 38761 ms · 2026-05-18T19:15:18.382107+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We demonstrate the equivalence between parameters of the two most widely used methods for analyzing this type of dynamic HFI... defect formation energy analysis as a function of the charge state of the Cd impurity... stable final EFG for the expected interaction HFIu originates from 111Cd probes located at defect-free substitutional Al sites (without trapped electron holes)

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    predicted V33 at the Cd site in Al2O3:Cdx- as a function of the charge of the impurity... comparison of predicted V33... with the experimental V33 values

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    A. G. Bibiloni, C. P. Massolo, J. Desimoni, L. A. Mendoza-Zélis, F. H. Sánchez, A. F. Pasquevich, L. Damonte, and A. R. López-García, Phys. Rev. B 32, 2393 (1985)

    work page 1985

  2. [2]

    C. P. Massolo, J. Desimoni, A. G. Bibiloni, L. A. Mendoza-Zélis, L. C. Damonte, A. R. Lopez-García, P. W. Martin, S. R. Dong, and J. G. Hooley, Phys. Rev. B 34, 8857 (1986)

    work page 1986

  3. [3]

    Bolse, M

    W. Bolse, M. Uhrmacher, and J. Kesten, Hyperfine Interact. 35, 931 (1987)

    work page 1987

  4. [4]

    K. Asai, F. Ambe, S. Ambe, T. Okada, and H. Sekizawa, Phys. Rev. B 41, 6124 (1990)

    work page 1990

  5. [5]

    Bartos, K

    A. Bartos, K. P. Lieb, A. F. Pasquevich, and M. Uhrmacher, Phys. Lett. A 157, 513 (1991)

    work page 1991

  6. [6]

    Lupascu, S

    D. Lupascu, S. Habenicht, K.-P. Lieb, M. Neubauer, M. Uhrmacher, and T. Wenzel, Phys. Rev. B 54, 871 (1996)

    work page 1996

  7. [7]

    Habenicht, D

    S. Habenicht, D. Lupascu, M. Uhrmacher, L. Ziegeler, and K.-P. Lieb, Z. Phys. B 101, 187 (1996)

    work page 1996

  8. [8]

    Habenicht, D

    S. Habenicht, D. Lupascu, M. Neubauer, M. Uhrmacher, K. P. Lieb, and the ISOLDE- Collaboration, Hyperfine Interact. 120, 445 (1999)

    work page 1999

  9. [9]

    Penner and R

    J. Penner and R. Vianden, Hyperfine Interact. 158, 389 (2004)

    work page 2004

  10. [10]

    G. N. Darriba, E. L. Muñoz, A. W. Carbonari, and M. Rentería, J. Phys. Chem. C 122, 17423 (2018)

    work page 2018

  11. [11]

    G. N. Darriba, E. L. Muñoz, D. Richard, A. P. Ayala, A. W. Carbonari, H. M. Petrilli, and M. Rentería, Phys. Rev. B 105, 195201 (2022)

    work page 2022

  12. [12]

    Bäverstam, R

    U. Bäverstam, R. Othaz, N. de Sousa, and B. Ringström, Nucl. Phys. A 186, 500 (1972)

    work page 1972

  13. [13]

    Iwatschenko-Borho, W

    M. Iwatschenko-Borho, W. Engel, H. Foettinger, D. Forkel, F. Meyer, and W. Witthuhn, Nucl. Instrum. Methods Phys. Res. B 7–8, 128 (1985)

    work page 1985

  14. [14]

    G. K. H. Madsen, P. Blaha, K. Schwarz, E. Sjöstedt, and L. Nordström, Phys. Rev. B 64, 195134 (2001)

    work page 2001

  15. [15]

    Frauenfelder and R

    H. Frauenfelder and R. M. Steffen, Alpha-, Beta-, and Gamma-Ray Spectroscopy, K. Seigbahn, Vol. 2 (North-Holland Publishing Co., Amsterdam, Netherland, 1968)

    work page 1968

  16. [16]

    E. N. Kaufmann and R. J. Vianden, Rev. Mod. Phys. 51, 161 (1979)

    work page 1979

  17. [17]

    Schatz and A

    G. Schatz and A. Weidinger, Nuclear Condensed Matter Physics: Nuclear Methods and Aplications (Wiley, Chichester, England, 1996)

    work page 1996

  18. [18]

    L. A. Mendoza-Zélis, A. G. Bibiloni, M. C. Caracoche, A. R. López-García, J. A. Martínez, R. C. Mercader, and A. F. Pasquevich, Hyperfine Interact 3, 315 (1977)

    work page 1977

  19. [19]

    Abragam and R

    A. Abragam and R. V. Pound, Phys. Rev. 92, 943 (1953)

    work page 1953

  20. [20]

    A. F. Pasquevich and M. Rentería, in Defects and Difussion Studied Using PAC Spectroscopy, edited by H. Jaeger and M.O. Zacate (Trans Tech Publications Ltd, Zurich, Switzerland, 2011), pp. 62-104, https://main.scientific.net/book/defects-and-diffusion-studied- using-pac-spectroscopy/978-3-03813-516-6/ebook

    work page 2011

  21. [21]

    Winkler and E

    H. Winkler and E. Gerdau, Z. Physik 262, 363 (1973)

    work page 1973

  22. [22]

    Winkler, γ-γ Angular correlations perturbed by randomly reorienting hyperfine fields, Z

    H. Winkler, γ-γ Angular correlations perturbed by randomly reorienting hyperfine fields, Z. Physik A 276, 225 (1976)

    work page 1976

  23. [23]

    25th Anniversary of Hyperfine interactions at La Plata

    M. Uhrmacher, M. Neubahuer, D. Lupascu, and K. P. Lieb, in Proceedings of the International Workshop “25th Anniversary of Hyperfine interactions at La Plata”, 1995 (Departamento de Física, UNLP, La Plata, 1995), p. 82

    work page 1995

  24. [24]

    Izumi, H

    F. Izumi, H. Asano, H. Murata, and N. Watanabe, J. App. Crystallogr. 20, 411 (1987)

    work page 1987

  25. [25]

    G. N. Darriba, M. Rentería, H. M. Petrilli, and L. V. C. Assali, Phys. Rev. B 86, 075203 (2012)

    work page 2012

  26. [26]

    Lucht, M

    M. Lucht, M. Lerche, H.-C. Wille, Y. V. Shvyd’ko, H. D. Rüter, E. Gerdau, and P. Becker, J. Appl. Cryst. 36, 1075 (2003)

    work page 2003

  27. [27]

    Blaha, K

    P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, and J. Luitz, WIEN2k, an Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties (Technical Universität, Wien, Austria, 2014)

    work page 2014

  28. [28]

    P. E. Blöchl, Phys. Rev. B 50, 17953 (1994)

    work page 1994

  29. [29]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)

    work page 1996

  30. [30]

    Schwarz, C

    K. Schwarz, C. Ambrosch-Draxl, and P. Blaha, Phys. Rev. B 42, 2051 (1990)

    work page 2051

  31. [31]

    Blaha, K

    P. Blaha, K. Schwarz, and P. H. Dederichs, Phys. Rev. B 37, 2792 (1988)

    work page 1988

  32. [32]

    Herzog, K

    P. Herzog, K. Freitag, M. Reuschenbach, and H. Walitzki, Z. Physik A 294, 13 (1980)

    work page 1980

  33. [33]

    A. P. Ayala, Program TDPAC, code developed to fit multiple-sites perturbation factors for static and dynamic hyperfine interactions in TDPAC experiments on polycrystalline samples, Ph.D. thesis, Universidad Nacional de La Plata, La Plata, Argentina, 1995

    work page 1995

  34. [34]

    Lohstroh, M

    A. Lohstroh, M. Uhrmacher, P.-J. Wilbrandt, H. Wulff, L. Ziegeler, and K. P. Lieb, Hyperfine Interact. 159, 35 (2004)

    work page 2004

  35. [35]

    E. L. Muñoz, D. Richard, A. W. Carbonari, L. A. Errico, and M. Rentería, Hyperfine Interact. 197, 199 (2010)

    work page 2010

  36. [36]

    E. L. Muñoz, Ph.D. thesis, Universidad Nacional de La Plata, La Plata, Argentina, 2011, available on line at http://sedici.unlp.edu.ar/handle/10915/2628

    work page 2011

  37. [37]

    K. W. Kehr, Hyperfine Interact. 17, 63 (1984)

    work page 1984